Perspectives in measuring the PPN parameters beta and gamma in the Earth's gravitational fields with the CHAMP/GRACE models

TL;DR

This paper explores the potential of using CHAMP and GRACE gravity models with drag-free spacecraft to measure PPN parameters beta and gamma in Earth's gravitational field with unprecedented accuracy, also enabling gravitomagnetic effect detection.

Contribution

It demonstrates that current gravity models can achieve high-precision tests of general relativity parameters using spacecraft, outlining the technological requirements and potential for improved measurements.

Findings

Gravity models from CHAMP and GRACE can reduce systematic errors to 10^-5.

Drag-free sensors with spectral noise density of 10^-8-10^-9 cm s^-2 Hz^-1/2 are needed.

Independent measurement of Lense-Thirring effect with 0.9% accuracy is feasible.

Abstract

The current bounds on the PPN parameters gamma and beta are of the order of 10^-4-10^-5. Various missions aimed at improving such limits by several orders of magnitude have more or less recently been proposed like LATOR, ASTROD, BepiColombo and GAIA. They involve the use of various spacecraft, to be launched along interplanetary trajectories, for measuring the effects of the solar gravity on the propagation of electromagnetic waves. In this paper we investigate what is needed to measure the combination nu=(2+2gamma-beta)/3 of the post-Newtonian gravitoelectric Einstein perigee precession of a test particle to an accuracy of about 10^-5 with a pair of drag-free spacecraft in the Earth's gravitational field. It turns out that the latest gravity models from the dedicated CHAMP and GRACE missions would allow to reduce the systematic error of gravitational origin just to this demanding level of accuracy. In regard to the non-gravitational errors, the spectral noise density of the drag-free sensors required to reach such level of accuracy would amounts to 10^-8-10^-9 cm s^-2 Hz^-1/2 over very low frequencies. Although not yet obtainable with the present technologies, such level of compensation is much less demanding than those required for, e.g., LISA. As a by-product, an independent measurement of the post-Newtonian gravitomagnetic Lense-Thirring effect with a 0.9% accuracy would be possible as well. The forthcoming Earth gravity models from CHAMP and GRACE will further reduce the systematic gravitational errors in both of such tests.